6.7-6.8 Method of Sections

Statics Lecture 25: Internal forces -- Introduction and Method of Sections

Statics Lecture 24: Simple truss analysis -- method of sections

Method of Sections

Truss Analysis: Method of Sections

Examples:

6.43, 6.53, 6.70

HW:
6.44, 6.54, 6.72

6.1-6.6 Analysis of Structures! Method of Joints

Statics Lecture 22: Simple truss analysis -- introduction (revised 3-4-13)

Statics Lecture 23: Simple truss analysis -- method of joints

Truss Example-Method of Joints

6.1

Single Rigid body with external forces → Several connected parts with internal forces

Simple Truss:
            m = 2n - 3

m = number of members
n = the total number of joints


6.4 Method of Joints:

The "You don't know what you've got until it's gone" method.

 - just image what would happen if one of the members was gone...

- nothing changes?  the member you removed was a zero force member.


- the truss collapses inward? then it must have been a compression member.



- the truss falls outwward?  it must have been a tension member.

Class Examples: 6.1, 6.4, 6.9

HW:
6.3, 6.5, 6.10

Chapt 5 overview + additional resources

Center of Mass Youtubes:

Just for fun - MIT Physics Demo -- Center of Mass Trajectory

Centroid

Kahn Academy - Center of Mass

Finding resultants of distributed beam loading conditions.

 Fluid Mechanics: Introduction to Forces on Planar and Submerged Surfaces

Fluid Mechanics: Forces on Curved Surfaces: Example 1

https://www.youtube.com/watch?v=E8EQ8uYMB88 

 https://www.youtube.com/watch?v=-adMiG0hyBM

centroid of the volume obtained by rotating the shaded area about the x-axis

Quiz:
1.  Locate the centroid of the plane area (similar to problems 5.1-5.16)
2.  For a given Distributed load, find a) the magnitude and location of the resultant, b) reactions at supports.  (similar to problems 5.66-5.95)
3.)  Locate the center of gravity for a 3D object (similar to problems 5.96-5.121)
Extra Credit: Locate the centroid of a volume created by rotating an area about an axis. (similar to problems 5.125-5.129)

5.10Centroids of Volumes, 5.11 composite Bodies, 5.12 Volumes by Integration

Examples:

HW:

 y=-(2h^2-3b^2)/(2(4h-3b))

 x=0.1402, y=0.0944, z=0.0959

 x=0.410, y=0.510, z=0.15

y=0, z=0, x=2.34

5.8 Loads on Beams 5.9 Forces on Submerged surfaces

Example:

 

 

 

Examples:

 

HW